{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singlet Lens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from optiland import optic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialization empty 'Optic' object, which is the core class in Optiland representing an optical system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "lens = optic.Optic()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add surfaces, one at a time. We define the surfaces as follows:\n",
    "\n",
    "1. Object surface at infinity.\n",
    "2. Convex surface with radius of curvature of 20 mm, lens material is N-SF11, and thickness is 5 mm.\n",
    "3. Planar surface with thickness to image plane of 23.0 mm.\n",
    "4. Image surface, which is planar (default).\n",
    "\n",
    "We assign the first lens surface at index 1 as the aperture stop surface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add surfaces\n",
    "lens.add_surface(index=0, thickness=np.inf)\n",
    "lens.add_surface(index=1, thickness=7, radius=20.0, is_stop=True, material=\"N-SF11\")\n",
    "lens.add_surface(index=2, thickness=23.0)\n",
    "lens.add_surface(index=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add the aperture. We choose entrance pupil diameter (EPD) as the aperture type and choose a value of 20 mm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add aperture\n",
    "lens.set_aperture(aperture_type=\"EPD\", value=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the field type to angle and define a single field at 0 degrees, i.e., on-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add field\n",
    "lens.set_field_type(field_type=\"angle\")\n",
    "lens.add_field(y=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add a single wavelength at 0.55 microns. Set this as the primary wavelength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add wavelength\n",
    "lens.add_wavelength(value=0.55, is_primary=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "View the system in 2D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lens.draw(num_rays=10)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
